


"""simple docstring"""



from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def      UpperCAmelCase     (       _lowercase :   NDArray[floataa]			,   _lowercase :   NDArray[floataa]			,   _lowercase :   list[int]			,   _lowercase :   int			,   )						-> list[float]:


	"""simple docstring"""




	lowerCAmelCase_							,	lowerCAmelCase_      							=			coefficient_matrix.shape
	lowerCAmelCase_							,	lowerCAmelCase_      							=			constant_matrix.shape

	if rowsa != colsa:
		lowerCAmelCase_      							=			F"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
		raise ValueError(_lowercase	)

	if colsa != 1:
		lowerCAmelCase_      							=			F"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
		raise ValueError(_lowercase	)

	if rowsa != rowsa:
		lowerCAmelCase_      							=			(
		    '''Coefficient and constant matrices dimensions must be nxn and nx1 but '''
		    F"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
		)
		raise ValueError(_lowercase	)

	if len(_lowercase	) != rowsa:
		lowerCAmelCase_      							=			(
		    '''Number of initial values must be equal to number of rows in coefficient '''
		    F"""matrix but received {len(_lowercase	)} and {rowsa}"""
		)
		raise ValueError(_lowercase	)

	if iterations <= 0:
		raise ValueError('''Iterations must be at least 1'''	)

	lowerCAmelCase_      							=			np.concatenate(
	    (coefficient_matrix, constant_matrix)			,   axis=1	)

	lowerCAmelCase_							,	lowerCAmelCase_      							=			table.shape

	strictly_diagonally_dominant(_lowercase	)

	# Iterates the whole matrix for given number of times
	for _ in range(_lowercase	):
		lowerCAmelCase_      							=			[]
		for row in range(_lowercase	):
			lowerCAmelCase_      							=			0
			for col in range(_lowercase	):
				if col == row:
					lowerCAmelCase_      							=			table[row][col]
				elif col == cols - 1:
					lowerCAmelCase_      							=			table[row][col]
				else:
					temp += (-1) * table[row][col] * init_val[col]
			lowerCAmelCase_      							=			(temp + val) / denom
			new_val.append(_lowercase	)
		lowerCAmelCase_      							=			new_val

	return [float(_lowercase	) for i in new_val]
def      UpperCAmelCase     (       _lowercase :   NDArray[floataa]	)						-> bool:


	"""simple docstring"""




	lowerCAmelCase_							,	lowerCAmelCase_      							=			table.shape

	lowerCAmelCase_      							=			True

	for i in range(0			,   _lowercase	):
		lowerCAmelCase_      							=			0
		for j in range(0			,   cols - 1	):
			if i == j:
				continue
			else:
				total += table[i][j]

		if table[i][i] <= total:
			raise ValueError('''Coefficient matrix is not strictly diagonally dominant'''	)

	return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
		import doctest

		doctest.testmod()



"""simple docstring"""



from diffusers.utils.testing_utils import require_onnxruntime







@require_onnxruntime
class    __a						:
				pass